Quantitative characteristic mode far-field relations in analyzing unidirectional high-directive ESAs

It's been examined that for electrically small antennas (ESAs) giving a high-directive (D≥4.77dBi) unidirectional pattern, at least two characteristic modes (CMs) should be excited. This behavior can be interpreted by our derived quantitative point symmetric relations of characteristic mode far-fields in this paper. The CM analysis of directivity leads to devising optimization objective functions, and further get simplified by using the above CM field relations, for unidirectional high-directive antenna design.